Lucas Z. Zhang
arXiv 12 Aug 2025 · Econometrics
arXiv:2508.09278 · PDF · Extracted main text
Motivated by the orthogonal series density estimation in $L^2([0,1],\mu)$, in this project we consider a new class of functions that we call the approximate sparsity class. This new class is characterized by the rate of decay of the individual Fourier coefficients for a given orthonormal basis. We establish the $L^2([0,1],\mu)$ metric entropy of such class, with which we show the minimax rate of convergence. For the density subset in this class, we propose an adaptive density estimator based on a hard-thresholding procedure that achieves this minimax rate up to a $\log$ term.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Lorentz, G. G (1966) Metric entropy and approximation | 1.000 | 10 | 4 | 100% |
| 2 | Belloni, A., Chernozhukov, V., Chetverikov, D., Hansen, C., and Kato… (2018) High-dimensional econometrics and regularized GMM | 1.000 | 9 | 4 | 100% |
| 3 | Yang, Y. and Barron, A (1999) Information-theoretic determination of minimax rates of convergence | 1.000 | 8 | 3 | 100% |
| 4 | Smolyak, S. A (1960) The $$-entropy of classes $E_s^,k(B)$ and $W_s^(B)$ in metric $L^2$ | 0.874 | 5 | 2 | 100% |
| 5 | Bousquet, O (2003) Concentration inequalities for sub-additive functions using the entropy method | 0.843 | 3 | 3 | 100% |
| 6 | Gajek,L (1986) On improving density estimators which are not bona fide functions | 0.811 | 4 | 2 | 100% |
| 7 | Bunea, F., Tsybakov, A. B., Wegkamp, M. H., and Barbu, A (2010) Spades and mixture models | 0.737 | 3 | 2 | 100% |
| 8 | Tsybakov, A. B (2008) Introduction to Nonparametric Estimation | 0.737 | 3 | 2 | 100% |
| 9 | Belloni, A., Chernozhukov, V., Chetverikov, D., and Hansen, C (2012) Sparse models and methods for optimal instruments with an application to eminent domain | 0.644 | 2 | 2 | 100% |
| 10 | Efromovich, S. Y (2008) Nonparametric Curve Estimation: Methods, Theory, and Applications | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 31 scored citations.